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The ability to predict the Remaining Useful Life (RUL) of Rotating Machines is a highly desirable function of Automated Condition Monitoring (ACM) systems. Typically, vibration signals are acquired through contact with the machine and used for monitoring. In this paper, a novel implementation of the ubiquitous feature extraction approach Envelope Analysis (EA) is applied to acoustic noise signals (< 25 kHz) to predict the RUL of a rotating machine. A well known drawback of the EA approach is that the frequency band of interest must be known or pre-estimated. Therefore, this approach is compared to a Data-Driven approach to feature extraction which utilizes an Information Theoretic approach to feature selection that does not require any a-priori information regarding the frequency band of interest. It is shown that the Data- Driven approach, with an accuracy of 97.7%, significantly outperforms the EA approach, with an accuracy of 93.7%. This study also shows that the improved performance of the Data-Driven approach is due to new information being uncovered in spectral locations across the entire spectrum from 0 to 25 kHz, and not just within one frequency band typically used by the EA approach.